Optimal Shape Design for Polymer Electrolyte Membrane Fuel Cell Cathode Air Channel: Modelling, Computational and Mathematical Analysis
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Bibliographic record
Abstract
Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right.\n\nThe second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it